Learning Intention: To understand Rates of Change and how calculus is used to study the motion of objects (kinematics). Success Criteria: Solve problems which involve distance, speed and acceleration using differentiation and integration

dy/dx is the rate of change of y with respect to x. Gradient of a line is the measure of how quickly y is changing in relation to x. dy/dx is the rate of change of y with respect to x. Use this concept for other variables. The area covered by a chemical spillage at a given time of t in seconds is given by A = t(t2 - 2) m2, t>2. The rate of change of the area covered, A, with respect to the time, t, is dA/dt. If A = t(t2 - 2) = t3 – 2t Then dA/dt = 3t2 – 2 E.g. the rate at which the area covered by the chemical spill is changing after 12 seconds is dA/dt = 3× 122 – 2 = 430m2/s dx

Kinematics – study of motion Velocity(speed) is the rate of change of distance with respect to time Distance is termed, s.Units for distance (s) is ____ Velocity, v = ds/dt units _____ Acceleration is the rate of change of ______ with respect to time. a = dv/dt units ______ In a practical context, where does motion normally start from? Origin Usually Horizontal motion If motion is vertical, origin is ground level ‘Initially’ means at time t=0, ie, when motion usually starts. Positive motion means above or to the right of the origin Negative motion – below or to the left of the origin When s = 0, the object is at the origin. Velocity Positive velocity – right or up Negative velocity – left or down If the velocity is zero, ie, v=0 then the object is stationary, or ‘at rest’. Acceleration Positive – speeding up Negative – slowing down If a = 0, the object is travelling at a constant speed. e.g. 17.02A on board

Objects hit or thrown through the air have vertical and horizontal velocity components (physics-kinematics). Use this info the calculate times to targets and distances vy vx 260m Vy is affected by gravity, which is the acceleration due to gravity. Vx is not affected by acceleration due to gravity. a = -10m/s2 Remember you can use v = s t